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Y’all should read this rn

Not a neural network, but still with a bunch of layers. Happy New Year! News are coming

🤔 What did we find? Different patterns produce small discrepancies in model predictions, but healthy and diseased microbiomes still cluster distinctly in the λ and σ space, showing fundamentally different ecological dynamics! 5/n

How do healthy (blue) and diseased (red) microbiomes look like, when we consider the inferred parameters? There's a lot to say, but stay with me, and consider the following plot [9/n]

Similarly to the magnetization of the Ising model, we have some order parameters, describing some coarse-grained statistics of the community (e.g. mean abundance) and require to average both over the species and over the disorder. Here's the key intuition of our work... [6/n]

To link the theory and data, we rely on previous results. Using the magic of replica-trick formalism the theory admits a mean-field Hamiltonian formulation. This formalism allows us to trade complexity (S species) with one species with random potential (here's \zeta!)

Inspired by Robert May's approach, we draw the interactions from a normal distribution choosing carefully the scaling of the mean and the variance with S. Albeit crude, this assumption leads to a dramatic reduction of the parameters to infer from O(S^2) to just O(1)! [4/n]

Lotka-Volterra model is a cornerstone of theoretical ecology, describing how the abundances of a local pool of species (S) evolve in time. However, it is typically unfeasible to fit all the O(S^2) parameters, especially with metagenomic data. What's the problem? [2/n]

This and only this

Here’s San Marco (Venice) and Sant Antonio (Padova)